Question

1. A store sells 12 different kinds of bathtubs. These data represent the maximum number of liters of water that the bathtubs will hold. 240, 272, 280, 285, 295, 285, 300, 290, 310, 305, 285, 305 (a) Compute the five-number summary for these data. Show all your work. (b) Identify all outliers of the data set. Use the values of the upper and lower fences to explain your answer. (c) Create a modified box plot for the bathtub data.

Answer 1

The given values are:

240,272,280,285,295,285,300,290,310,305,285,305

with n=12.

The sorted set of numbers is:

240 272 280 285 285 285 290 295 300 305 305 310

minimum = 240

Q1 = 282.5

median = 287.5

Q3 = 302.5

maximum = 310

the five-number summary is (240,282.5,287.5,302.5,310)

The interquartile range (IQR) = Q3-Q1 = 20

We proceed to calculate the lower and upper fences.

Lower fence = Q1-1.5(IQR)=252.5

Upper fence = Q3+1.5(IQR)=332.5

Since 240 falls below the lower fence (252.5), we conclude that 240 is an outlier, it should be eliminated from the data and the above calculations repeated.

272 280 285 285 285 290 295 300 305 305 310

and five-number summary:

272.0 285.0 290.0 302.5 310.0

1.5IQR = (302.5-285) = 26.25

and the fences are:

Lower fence = 285-26.25 = 258.75

Upper fence = 302.5 + 26.25 = 328.75

Since this time around, no data falls outside of the fences

(check: min=272>258.75, max=310<328.75)

We conclude that there are no more outliers in this trimmed list

272 280 285 285 285 290 295 300 305 305 310